I don't share the same sentiment as some of the others... I would heavily recommend a new diff carrier. I think that you may be in luck as the complete assembly (As of recently) was still available from the dealer. Check 41110-60370 as it is a brand new front locking differential assembly including the locking actuator (Not 100% on that).
If those case hardened gears IE: ring and pinion plus spider gears, have been run with zero lubrication, there is no way those gears will last. I can guarentee even though you haven't put many miles on the truck, the damage is done and your gears are scored. They are either going to make noise when fully rebuilt or not, but they will no way retain their hardness and will likely lead to constant backlash problems and produce metal shavings until their untimely demise. If it was a trail buggy i'd say throw bearings in it and pin it.
Because everything has been run dry the gears and bearings have created much more heat than designed, which means everything has expanded that heat into the carrier housing. You have already possibly spun a carrier bearing in the diff even with the light driving. Long story short you WILL NOT get a good pattern and you WILL NOT get any sort of good life expectancy out of the diff from the assembly being run dry. I would not accept a rebuild if it were me. Because if they throw new gears in the carrier it may actually last a while (Long enough for them to walk away from their mistake) but not last many many thousands of miles as you will have constant metal being produced from things not running true inside the diff. The reason East coast gives you explicit instructions when you buy a set of gears from them is not just because it's good practice, it's because new gear sets create a lot of extra heat as they "Bed" themselves together creating a perfect surface hardness and toast the gear oil and produce break in shavings that must be changed out after the first 500 miles. That surface hardness is what makes those gears last the life of the vehicle under normal circumstances.
If those case hardened gears IE: ring and pinion plus spider gears, have been run with zero lubrication, there is no way those gears will last. I can guarentee even though you haven't put many miles on the truck, the damage is done and your gears are scored. They are either going to make noise when fully rebuilt or not, but they will no way retain their hardness and will likely lead to constant backlash problems and produce metal shavings until their untimely demise. If it was a trail buggy i'd say throw bearings in it and pin it.
Because everything has been run dry the gears and bearings have created much more heat than designed, which means everything has expanded that heat into the carrier housing. You have already possibly spun a carrier bearing in the diff even with the light driving. Long story short you WILL NOT get a good pattern and you WILL NOT get any sort of good life expectancy out of the diff from the assembly being run dry. I would not accept a rebuild if it were me. Because if they throw new gears in the carrier it may actually last a while (Long enough for them to walk away from their mistake) but not last many many thousands of miles as you will have constant metal being produced from things not running true inside the diff. The reason East coast gives you explicit instructions when you buy a set of gears from them is not just because it's good practice, it's because new gear sets create a lot of extra heat as they "Bed" themselves together creating a perfect surface hardness and toast the gear oil and produce break in shavings that must be changed out after the first 500 miles. That surface hardness is what makes those gears last the life of the vehicle under normal circumstances.